Traditional linear multiscale representations of discretized
images describe an image as a sum of translated and scaled copies of a set
of basis functions. The steerable pyramid is an example of such a representation
where the basis functions used are derivative operators, and the subbands
are then gradients of progressively blurred copies of the original image.

In this talk, I present a nonlinear representation based on the steerable
pyramid where only the orientation of the gradient is kept, and all of the
magnitude information is discarded. The representation is thus entirely based
on measurements of local geometry of the image. Surprisingly, I am able to
recover the original image from only the orientation information. I
will describe the basic iterative reconstruction algorithm and some tricks
to speed up its convergence. At the end I will discuss some ongoing issues
in using this novel representation as a tool for image processing.